Law and order could be maintained if the police break into stores and distribute items in an orderly fashion, playing "Soup Nazi" if need be. Even if some people truly need certain items, they're no more likely to actually get the items they truly need in a free-for-all than they would be if looting/'finding'/etc. were effectively prohibited. Having police distribute items in semi-controlled fashion would be better than either alternative.
There was one store doing that I saw on the news, and it has not been looted largely as a result. People are getting fed, and the store survives.